# Microwave spectroscopy of radio-frequency dressed $^{87}$Rb

## TL;DR

This paper investigates the hyperfine spectrum of $^{87}$Rb atoms under radio-frequency dressing across various trapping conditions, revealing resonant side bands and demonstrating precise control and measurement capabilities.

## Contribution

It provides a comprehensive experimental and theoretical analysis of RF-dressed $^{87}$Rb spectra in different trapping scenarios, including a semi-classical model and practical applications.

## Key findings

- Observation of resonant side bands spaced by the dressing frequency
- Theoretical explanation using semi-classical model and Rotating Wave Approximation
- Demonstration of accurate determination of dressing configuration and microwave field

## Abstract

We study the hyperfine spectrum of atoms of $^{87}$Rb dressed by a radio-frequency field, and present experimental results in three different situations: freely falling atoms, atoms trapped in an optical dipole trap and atoms in an adiabatic radio-frequency dressed shell trap. In all cases, we observe several resonant side bands spaced (in frequency) at intervals equal to the dressing frequency, corresponding to transitions enabled by the dressing field. We theoretically explain the main features of the microwave spectrum, using a semi-classical model in the low field limit and the Rotating Wave Approximation for alkali-like species in general and $^{87}$Rb atoms in particular. As a proof of concept, we demonstrate how the spectral signal of a dressed atomic ensemble enables an accurate determination of the dressing configuration and the probing microwave field.